I'd normally use embedded myself, but I'm not convinced imbedded would exactly be "wrong", even allowing for the fact that embedded has become far more popular in recent decades (primarily in technical contexts, I suspect).
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FumbleFingersJun 17 '12 at 16:55

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@FumbleFingers: I now see that OED gives 'imbedded' as an alternative spelling.
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Barrie EnglandJun 17 '12 at 17:48

Imbed is an alternative spelling of embed, and the relevant meaning of embed is the second sense in wiktionary's entry: "(by extension) To include in surrounding matter. [e.g.]
We wanted to embed our reporter with the Fifth Infantry Division, but the Army would have none of it."

That is, the latter half of the example sentence means "are involved in the internet", "are included in the internet", or "are integrated into the internet". The general meaning of the example is "I know how deeply your activities are part of [or depend upon] the internet".

Embedded means to integrate into, like embedding a jewel in a setting or a nail in a wall perhaps (this would imply the whole thing had been hammered in). A person can not be embedded in the internet as that would imply physical enplanting - i.e. being totally surrounded physically by the internet (which is not physical).

I think you can use imbedded but if you do, strengthen the sentence by tossing out deeply. (imbed implies depth) When not used technically, embedded has taken on political connotations as in "embedded journalist". So you might want to use a relatively neutral word such as "engrossed" or "enamored".